Spin axis reorientation maneuvers are utilized, over a spinning transfer orbit and during a mission, to position a satellite in a proper Perigee/Apogee burn attitude or a proper liquid apogee motor (LAM) burn attitude. A spin axis reorientation maneuver may also be utilized to change the sun polar angle of the satellite to provide favorable power and thermal conditions. The satellite spin axis can be reoriented via control of onboard thrusters.
To perform a reorientation maneuver, a satellite controller compares a target attitude with an initial or estimated attitude to determine an angle error therebetween. The commanded and estimated attitudes are often represented by quaternions. The angular error signal can be represented by an error quaternion, or be referred to as the Euler angle by small angle approximation. The satellite then performs a closed-loop reorientation maneuver using the angular error to generate an acceleration command signal is converted into torque generated by the thrusters and exerted on the satellite, which in effect moves the spin axis of the satellite toward a target orientation. Ability to precisely control the spin axis trajectory during the reorientation maneuver, or in effect, the movement of the satellite spin axis in inertial space, is highly desirable. Improved control of the spin axis trajectory can provide an increase in maneuver flexibility and accuracy, as well as simplify fault protection design and, as well as fuel efficiency.
In particular, a “minimum-angle” slew is often desired. Minimum-angle slew refers to the rotating of the spin axis about an axis that is normal to both a first unit vector, along the initial spin axis, and a second unit vector, along the target spin axis. In performing a minimum angle slew, the spin axis trajectory of the satellite follows an arc of a great circle, i.e., a generally non-curved, shortest distance path on along a perimeter of a sphere.
Several reorientation control methods have been utilized to reorient a satellite with minimum-angle rotation. The control methods tend to generate a control signal, which is directed about an instantaneous eigenaxis or along the direction of an instantaneous angular position error vector, and include the use of reorientation and rate tracking, and angle and rate limits. The instantaneous angular position error vector is the vector representation of attitude error. However, these control methods are limited to being performed when the satellite is in a non-spinning state and are incapable of controlling a spin axis trajectory during a reorientation maneuver.
In a non-spinning state, the eigenaxis of the satellite is fixed in the satellite body coordinate frame and is stationary in inertial space. The eigenaxis is the Euler axis about which a single rotation can be performed to change the attitude of a body between orientations. In the spinning state, the instantaneous eigenaxis, in the body frame, is changing constantly. The constant change in instantaneous eigenaxis prevents the spin axis from following a minimum-angle reorientation trajectory using the stated traditional control methods of reorientation.
Additionally, spin phase error ambiguity can negatively affect performance of a minimum-angle reorientation. An angular position error signal can be regarded as the composition of spin axis attitude error and spin phase error. The spin phase error refers to the angular error about the satellite spin axis. When the commanded and estimated attitudes are not synchronized in the spin phase, the direction of the position error vector is dependent on the magnitude of spin phase error. This is referred to as spin phase error ambiguity. The spin phase error ambiguity increases the difficulty in predicting the spin axis trajectory and maneuver time.
Thus, there exists a need for an improved satellite reorientation system that allows for the accurate control of the spin axis trajectory and that allows for minimum-angle slew to be performed along a path of minimum distance end-to-end.